Back to Departmental Colloquium: Spring 2023
Departmental Colloquium
Date: Thursday, Mar 23, 2023
Time: 4:00PM - 5:00PM
Location: JWB 335
Richard Tsai
University of Texas at Austin
Title |
Implicit boundary integral methods and applications |
Abstract |
I will review a general framework that can be used to develop numerical methods for various problems involving non-parametrically defined surfaces. The main idea is to formulate appropriate extensions of a given problem defined on a surface to ones in the narrow band of the surface in the embedding space. The extensions are arranged so that the solutions to the extended problems are equivalent, in a strong sense, to the surface problems that we set out to solve. Such extension approaches allow us to analyze the well-posedness of the resulting system, develop systematically and in a unified fashion numerical schemes for treating a wide range of problems involving differential and integral operators, and deal with similar problems in which only point clouds sampling the surfaces are given. We will demonstrate a few computations of some applications involving integral equations, partial differential equations, and optimal control problems on hypersurfaces. |
Applied Mathematics
Computational Mathematics